Now, why would illegal aliens have ANY say in the US immigration policy?

That would be like saying that the Zionist invaders of Palestinian lands have a right to say who gets to live in Palestine.

Get the H out of the USA and take a dump on someone elses' right to self determination.

Back when women didn't have the vote, they still had political influence.

Back when Blacks didn't have the vote, they still had political influence.

It seems like corporations around the world have influence on the US politicians, despite not having a right to vote.

People who aren't franchised are still legitimate political players. They can go on strike. They can create pressure. The Dream 9 are masterful.

What they are doing is offering political potential and alliance to the Democrats. It's not a foregone conclusion that they'll support the centrist Dems. They might opt to only do political work for progressives. That potential they have is what they're using.